sec^2x
To solve this equation, we will first use the identity:
1 + tan^2x = sec^2x
This is an identity that is always true for any value of x, so we can substitute it in for the left side of our equation:
1 + tan^2x = sec^2x
sec^2x = sec^2x
We can see that both sides of the equation are equal, so the original equation is true for any value of x. Therefore, our final answer is:
1 + tan^2x = sec^2x
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